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AllQuestion and Answers: Page 1854

Question Number 18546 Answers: 0 Comments: 2

In ΔABC, tan(A/2) + tan(B/2) + tan(C/2) = (√3), then Δ must be (1) Equilateral (2) Isosceles (3) Acute angled

$$\mathrm{In}\:\Delta{ABC},\:\mathrm{tan}\frac{{A}}{\mathrm{2}}\:+\:\mathrm{tan}\frac{{B}}{\mathrm{2}}\:+\:\mathrm{tan}\frac{{C}}{\mathrm{2}}\:=\:\sqrt{\mathrm{3}}, \\ $$$$\mathrm{then}\:\Delta\:\mathrm{must}\:\mathrm{be} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Equilateral} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Isosceles} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Acute}\:\mathrm{angled} \\ $$

Question Number 18545 Answers: 1 Comments: 0

The number of solutions of sin3x + cos2x = 0 in [0, ((3π)/2)] is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mathrm{sin3}{x}\:+\:\mathrm{cos2}{x}\:=\:\mathrm{0}\:\mathrm{in}\:\left[\mathrm{0},\:\frac{\mathrm{3}\pi}{\mathrm{2}}\right]\:\mathrm{is} \\ $$

Question Number 18543 Answers: 1 Comments: 0

Question Number 18538 Answers: 0 Comments: 0

Question Number 18530 Answers: 1 Comments: 0

In an atom the last electron is present in f-orbital and for its outermost shell the graph of Ψ^2 has 6 maximas. What is the sum of group and period of that element?

$$\mathrm{In}\:\mathrm{an}\:\mathrm{atom}\:\mathrm{the}\:\mathrm{last}\:\mathrm{electron}\:\mathrm{is}\:\mathrm{present} \\ $$$$\mathrm{in}\:{f}-\mathrm{orbital}\:\mathrm{and}\:\mathrm{for}\:\mathrm{its}\:\mathrm{outermost}\:\mathrm{shell} \\ $$$$\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\Psi^{\mathrm{2}} \:\mathrm{has}\:\mathrm{6}\:\mathrm{maximas}.\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{group}\:\mathrm{and}\:\mathrm{period}\:\mathrm{of}\:\mathrm{that} \\ $$$$\mathrm{element}? \\ $$

Question Number 19238 Answers: 0 Comments: 4

Let ABCD be a parallelogram. Two points E and F are chosen on the sides BC and CD, respectively, such that ((EB)/(EC)) = m, and ((FC)/(FD)) = n. Lines AE and BF intersect at G. Prove that the ratio ((AG)/(GE)) = (((m + 1)(n + 1))/(mn)).

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{parallelogram}.\:\mathrm{Two} \\ $$$$\mathrm{points}\:{E}\:\mathrm{and}\:{F}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{on}\:\mathrm{the}\:\mathrm{sides} \\ $$$${BC}\:\mathrm{and}\:{CD},\:\mathrm{respectively},\:\mathrm{such}\:\mathrm{that} \\ $$$$\frac{{EB}}{{EC}}\:=\:{m},\:\mathrm{and}\:\frac{{FC}}{{FD}}\:=\:{n}.\:\mathrm{Lines}\:{AE}\:\mathrm{and}\:{BF} \\ $$$$\mathrm{intersect}\:\mathrm{at}\:{G}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\frac{{AG}}{{GE}}\:=\:\frac{\left({m}\:+\:\mathrm{1}\right)\left({n}\:+\:\mathrm{1}\right)}{{mn}}. \\ $$

Question Number 19236 Answers: 1 Comments: 0

Question Number 18527 Answers: 0 Comments: 0

from 1 to 100 isn′t(10,20,30,40,50,60,70,80,90,100), totalizing 10 times the number 0 apears from 1 to 100?

$${from}\:\mathrm{1}\:{to}\:\mathrm{100}\:{isn}'{t}\left(\mathrm{10},\mathrm{20},\mathrm{30},\mathrm{40},\mathrm{50},\mathrm{60},\mathrm{70},\mathrm{80},\mathrm{90},\mathrm{100}\right),\:{totalizing}\:\mathrm{10}\:{times}\:{the}\:{number}\:\mathrm{0}\:{apears}\:{from}\:\mathrm{1}\:{to}\:\mathrm{100}? \\ $$

Question Number 18524 Answers: 2 Comments: 0

The number of solutions of the equation sin^3 x − 3sinxcos^2 x + 2cos^3 x = 0 in [−(π/4), (π/4)] is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}^{\mathrm{3}} {x}\:−\:\mathrm{3sin}{x}\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{2cos}^{\mathrm{3}} {x}\:=\:\mathrm{0}\:\mathrm{in} \\ $$$$\left[−\frac{\pi}{\mathrm{4}},\:\frac{\pi}{\mathrm{4}}\right]\:\mathrm{is} \\ $$

Question Number 18523 Answers: 0 Comments: 0

Match the following Column-I (Trigonometric equation) (A) sin 9θ = cos ((π/2) − θ) (B) sin 5θ = sin ((π/2) + 2θ) (C) cos 11θ = cos 3θ (D) 3 tan (θ − 15°) = tan (θ + 15°) Column-II (Family of solutions) (p) (2n + 1)(π/(10)), n ∈ Z (q) ((nπ)/2) + (−1)^n (π/4), n ∈ Z (r) ((nπ)/7), n ∈ Z (s) (4n + 1)(π/(14)), n ∈ Z

Question Number 18502 Answers: 1 Comments: 0

The second overtone of a fixed viberating string fixed at both end is 200cm. Find the length of the string.

$$\mathrm{The}\:\mathrm{second}\:\mathrm{overtone}\:\mathrm{of}\:\mathrm{a}\:\mathrm{fixed}\:\mathrm{viberating}\:\mathrm{string}\:\mathrm{fixed}\:\mathrm{at}\:\mathrm{both}\:\mathrm{end}\:\mathrm{is}\:\mathrm{200cm}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string}. \\ $$

Question Number 18498 Answers: 5 Comments: 1

How many times is digit 0 written when listing all numbers from 1 to 3333?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{is}\:\mathrm{digit}\:\mathrm{0}\:\mathrm{written}\:\mathrm{when} \\ $$$$\mathrm{listing}\:\mathrm{all}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{3333}? \\ $$

Question Number 18499 Answers: 0 Comments: 1

what is the in pounds of a vertical cylindrical tank that is 6ft in dia meter and 15ft in height.if it weig hs 20lbs per ft of height.

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{in}\:\mathrm{pounds}\:\mathrm{of}\:\mathrm{a}\:\mathrm{vertical} \\ $$$$\mathrm{cylindrical}\:\mathrm{tank}\:\mathrm{that}\:\mathrm{is}\:\mathrm{6ft}\:\mathrm{in}\:\mathrm{dia} \\ $$$$\mathrm{meter}\:\mathrm{and}\:\mathrm{15ft}\:\mathrm{in}\:\mathrm{height}.\mathrm{if}\:\mathrm{it}\:\mathrm{weig} \\ $$$$\mathrm{hs}\:\mathrm{20lbs}\:\mathrm{per}\:\mathrm{ft}\:\mathrm{of}\:\mathrm{height}. \\ $$

Question Number 18493 Answers: 1 Comments: 1

Draw the free body diagram of following system:

$$\mathrm{Draw}\:\mathrm{the}\:\mathrm{free}\:\mathrm{body}\:\mathrm{diagram}\:\mathrm{of}\:\mathrm{following} \\ $$$$\mathrm{system}: \\ $$

Question Number 18492 Answers: 1 Comments: 1

Question Number 18486 Answers: 0 Comments: 0

Why ionic radii of^(35) Cl <^(37) Cl^− ?

$$\mathrm{Why}\:\mathrm{ionic}\:\mathrm{radii}\:\mathrm{of}\:^{\mathrm{35}} \mathrm{Cl}\:<\:^{\mathrm{37}} \mathrm{Cl}^{−} ? \\ $$

Question Number 18477 Answers: 0 Comments: 0

F[topology]={G⊂X.G is finit.} please sol it

$$\mathscr{F}\left[{topology}\right]=\left\{{G}\subset{X}.{G}\:{is}\:{finit}.\right\} \\ $$$${please}\:{sol}\:{it} \\ $$

Question Number 18474 Answers: 1 Comments: 0

Assertion-Reason Type Question STATEMENT-1 : f(x) = log_(cosx) sinx is well defined in (0, (π/2)). and STATEMENT-2 : sinx and cosx are positive in (0, (π/2)).

$$\boldsymbol{\mathrm{Assertion}}-\boldsymbol{\mathrm{Reason}}\:\boldsymbol{\mathrm{Type}}\:\boldsymbol{\mathrm{Question}} \\ $$$$\mathrm{STATEMENT}-\mathrm{1}\::\:{f}\left({x}\right)\:=\:\mathrm{log}_{\mathrm{cos}{x}} \mathrm{sin}{x}\:\mathrm{is} \\ $$$$\mathrm{well}\:\mathrm{defined}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right). \\ $$$$\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\mathrm{sin}{x}\:\mathrm{and}\:\mathrm{cos}{x}\:\mathrm{are} \\ $$$$\mathrm{positive}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right). \\ $$

Question Number 18472 Answers: 1 Comments: 0

The general solution of 2^(sin x) + 2^(cos x) = 2^(1−(1/(√2))) is

$$\mathrm{The}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{2}^{\mathrm{sin}\:{x}} \:+\:\mathrm{2}^{\mathrm{cos}\:{x}} \\ $$$$=\:\mathrm{2}^{\mathrm{1}−\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}} \:\mathrm{is} \\ $$

Question Number 18466 Answers: 1 Comments: 0

The sum of the digits of a two digit number is 5 and their difference is 3. Find the number.

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit} \\ $$$$\mathrm{number}\:\mathrm{is}\:\mathrm{5}\:\mathrm{and}\:\mathrm{their}\:\mathrm{difference}\:\mathrm{is}\:\mathrm{3}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}. \\ $$

Question Number 18465 Answers: 1 Comments: 0

The sum of the digits of a two digit number is 5 and their difference is 3. Find the number.

Question Number 18464 Answers: 1 Comments: 0

3 numbers are chosen from 1 to 30. The probability that they are not consecutive is

$$\mathrm{3}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{30}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{they}\:\mathrm{are}\:\mathrm{not}\:\mathrm{consecutive} \\ $$$$\mathrm{is} \\ $$

Question Number 18463 Answers: 1 Comments: 0

The solid angle subtended by a spherical surface of radius R at its centre is (π/2) steradian, then the surface area of corresponding spherical section is

$$\mathrm{The}\:\mathrm{solid}\:\mathrm{angle}\:\mathrm{subtended}\:\mathrm{by}\:\mathrm{a}\:\mathrm{spherical} \\ $$$$\mathrm{surface}\:\mathrm{of}\:\mathrm{radius}\:{R}\:\mathrm{at}\:\mathrm{its}\:\mathrm{centre}\:\mathrm{is}\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{steradian},\:\mathrm{then}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{area}\:\mathrm{of} \\ $$$$\mathrm{corresponding}\:\mathrm{spherical}\:\mathrm{section}\:\mathrm{is} \\ $$

Question Number 18461 Answers: 1 Comments: 0

Question Number 18460 Answers: 1 Comments: 0

Question Number 18457 Answers: 1 Comments: 0

The number of solutions of the equation sin θ + cos θ = 1 + sin θ cos θ in the interval [0, 4π] is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}\:\theta\:+\:\mathrm{cos}\:\theta\:=\:\mathrm{1}\:+\:\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{interval}\:\left[\mathrm{0},\:\mathrm{4}\pi\right]\:\mathrm{is} \\ $$

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